Planetary gear mechanisms are employed in various kinds of reduction mechanism since they have a large reduction gear ratio and can bear a large transmission load. Of these planetary gear mechanisms, a known mechanism called a harmonic reduction gear is provided with two internally-toothed gears having mutually different numbers of teeth, a phase difference due to the difference in the number of teeth of the two internally-toothed gears is created for each rotation of an input shaft, by deflecting an annular externally-toothed gear which meshes with the internally toothed gears, and rotational speed is reduced by transmitting this phase difference to an output shaft. Such gear mechanisms are shown in Examined Publication Nos. 36137/75 and 46115/75, and Japanese Patent Examined Publication Nos. 32883/71 and 41172/70.
A more detailed description of this harmonic reduction gear will be given below.
Referring to FIGS. 1 and 2, an oval eccentric member 2 is fixed to an input shaft 1, and an annular externally-toothed gear 3 is slidably supported by the outer periphery of the eccentric member 2. The annular externally-toothed gear 3 is deflectable and meshes with internally-toothed gears (discribed below) at two portions on the long-diameter sides of the oval eccentric member 2, but does not mesh with the internally-toothed gear on the short-diameter sides thereof. Two internally-toothed gears 4, 5 are provided around the external periphery of the exterally-toothed gear 3, the internally-toothed gear 4 being secured to a casing 6 and the internally-toothed gear 5 being connected to an output shaft 7. In this embodiment, the number of teeth of the internally-toothed gear 4 is identical to that of the externally-toothed gear 3, and there is a small difference in the number of teeth between the internally-toothed gears 4 and 5.
In operation, when the eccentric member 2 eccentrically rotates once, the externally-toothed gear 3 meshes with the internally-toothed gears 4 and 5. Since the internally-toothed gear 4 is fixed, the internally-toothed gear 5 is displaced by a relative amount given by the difference in the number of teeth, the output shaft 7 rotates through an angle given by the difference in the number of teeth, and thus rotation of the input shaft 1 is transmitted to the output shaft 7 to cause the same to rotate at a reduced speed.
However, the meshing mechanism of the above-described conventional harmomic reduction gear has the drawbacks described below.
In the first place, the gear transmission mechanism provides faulty transmission based on play and backlash, so that rotation of the input shaft 1 is sometimes not transmitted directly as rotation of the output shaft 7. Such relative faulty transmission between the input shaft 1 and the output shaft 7 is hereafter called angular backlash.
Position-controlling reduction gears used in precision machinery such as industrial robots and machine tools are required to have a high reduction gear ratio and high efficiency, high rigidity, and low angular backlash characteristics.
Referring to FIG. 3, a tooth profile 8 of the externally-toothed gear 3 is a triangular or involute tooth profile, and the envelope of the locus of the tooth profile when the externally-toothed gear 3, which has the tooth profile 8, meshes with the internally-toothed gear 5, which has a different number of teeth, is determined by the locus of an angular portion 9 of the tooth profile 8. In other words, a tooth profile 10 of the internally-toothed gear 5 which provides low angular backlash is determined on the basis of the envelope drawn by the angular portion 9 of the tooth profile 8 of the externally-toothed gear 3. Accordingly, torque is transmitted to the tooth profile 10 via the angular portion 9 which forms an acute angle of the tooth profile 8, and the arrangement is such that the contact pressure acting on the working face is large, thereby reducing the life of the teeth.
In addition, as shown in FIG. 4, in the locus of the tooth profile 8 formed as the externally-toothed gear 3 meshes with the internally-toothed gear 4, which has the same number of teeth, a part of the tooth profile 8 does not form the envelope, and the tooth profile 8 is located in the outermost portion of the envelope only at a special meshing position (the tooth profile 8 is located on the innermost side of a tooth profile 11 of the internally-toothed gear 4). For this reason, the configuration of the tooth profile 11 of the internally-toothed gear 4 is determined by the position at which the tooth profile 8 of the externally-toothed gear 3 is located at the outermost portion of the envelope. Consequenty, a low angular backlash can be secured only at the position at which this tooth profile 8 is located at the outermost portion, and the gap between the tooth profile 8 and the tooth profile 11 gradually widens with distance from this position as a boundary, so that the externally-toothed gear 3 and the internally-toothed gear 4 become disengaged from each other, leading to a decline in the contact ratio of the entire gear. Consequently, the load borne by each tooth increases, with the result that the strength of the tooth drops and apparent angular backlash increases because of deformation of the teeth.
The above-described drawback also appears in the meshing of the precision fine-adjustment mechanism having the same tooth profile as the planetary gear mechanism, described previously and shown in FIG. 5. In such precision fine-adjustment mechanism, fine displacement by means of engagement between two linear racks and a pinion rack which is deflectable is provided. A reciprocating cam 32 is provided on a guideway 31 via roller bearings 33. A deflectable pinion rack 35 is provided on the cam 32 via roller bearings 34. The pinion rack 35 meshes with two linear racks 36, 37. The linear rack 36 is movable, but the linear rack 37 is fixed. The number of teeth per unit length of the linear rack 37 is identical to that of the pinion rack 35. The tooth pitch per unit length of the linear rack 36 is different from that of the linear rack 37.
Consequently, if the cam 32 slides a unit length, the displacement of the movable rack given by the phase difference in the tooth pitch between the two linear racks 37 and 36 is obtained.
The tooth profile of each of the racks used in the above-described precision fine-adjustment mechanism has the same configuration as the tooth profile of the planetary gear mechanism described previously, and has a similar drawback.
An object of the present invention is to provide a tooth profile in a meshing mechanism which ameliorates the drawback of the above-described meshing mechanisms and has a high reduction gear ratio and high efficiency, high rigidity, and low angular backlash characteristics.